CBSE Class 12-science Answered
Two spherical conductors A and B are having charge densities σA and σB respectively. If they are joined by a thin wire then what will be the ratio of charge densities finally if the radii are rA and rB.
Asked by hitanshu04 | 17 May, 2021, 21:09: PM
Charged spherical conductors are joined by thin wire , then they are at same potential.
K × ( qA / rA ) = K × ( qB / rB ) .........................(1)
where K = 1 / ( 4 π εo ) is Coulomb's constant, qA is charge on sphere-A , qB is charge on sphere-B,
rA is radius of sphere-A and rB is radius of sphere-B .
Hence from eqn.(1) , we get ,
![begin mathsize 14px style q subscript A over q subscript B space equals space r subscript A over r subscript B end style](https://images.topperlearning.com/topper/tinymce/cache/5ada082f4e12bddc3bd6a6e64926edea.png)
if
and
are charge densities respectively on sphere-A and sphere-B after connetcing by thin wire ,
![begin mathsize 14px style sigma subscript A apostrophe end style](https://images.topperlearning.com/topper/tinymce/cache/4c40f11b41742377c64237885939ae5b.png)
![begin mathsize 14px style sigma subscript B apostrophe end style](https://images.topperlearning.com/topper/tinymce/cache/a65f993b1d3816e2099e866a7a44ad98.png)
then we have , ![begin mathsize 14px style q subscript A over q subscript B space equals space fraction numerator 4 pi space r subscript A superscript 2 space sigma subscript A apostrophe over denominator 4 space pi space r subscript B superscript 2 space sigma subscript B apostrophe end fraction space equals space r subscript A over r subscript B end style](https://images.topperlearning.com/topper/tinymce/cache/409506a425bff1d0525d175b08d6265c.png)
![begin mathsize 14px style q subscript A over q subscript B space equals space fraction numerator 4 pi space r subscript A superscript 2 space sigma subscript A apostrophe over denominator 4 space pi space r subscript B superscript 2 space sigma subscript B apostrophe end fraction space equals space r subscript A over r subscript B end style](https://images.topperlearning.com/topper/tinymce/cache/409506a425bff1d0525d175b08d6265c.png)
Hence we get , ![begin mathsize 14px style fraction numerator space sigma subscript A apostrophe over denominator space sigma subscript B apostrophe end fraction space equals space r subscript B over r subscript A end style](https://images.topperlearning.com/topper/tinymce/cache/63966002511ac85216b63f3be1655442.png)
![begin mathsize 14px style fraction numerator space sigma subscript A apostrophe over denominator space sigma subscript B apostrophe end fraction space equals space r subscript B over r subscript A end style](https://images.topperlearning.com/topper/tinymce/cache/63966002511ac85216b63f3be1655442.png)
Answered by Thiyagarajan K | 17 May, 2021, 23:13: PM
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